Maths: Trigonometry 5 - Sine and Cosine Rules

Sine and cosine can be used on any triangle, not just right-angled triangles. But as there is no right angle, there is no hypotenuse, so different formulae are needed

Sine Rule

Notice that the small letters, for the lengths of the sides, are opposite to the corresponding capital letters for the angles.

So for this triangle…

You are given angles A and C and side c, so use

B=180-(60+45)=75 and now

So, if an angle and the length of its opposite side is known, then the other angles and sides can be worked out, using just one other length or angle. But be careful when the triangle is obtuse angled, because, for example, sin50 = sin130, that is…